Hi when I do the double integral dxdt x from L to 0 for E(phi).why after integration for x (L ) vanishes? I'm really confused.Could you please explain each step of your calculation and answer my question please.Thank you!!

6. (C) A string has its endpoints fixed at (0, 0) and (L, 0). If its height at a and time t is (x, t) then (to a good approximation) its total kinetic energy is E($) = " So didx and its total potential energy (coming from stretching tension) is T(d) = 5 So badx. The string moves to minimise the integral (E($) - T($) ) dt. Show that the string obeys the wave equation 2 at 2 2x2 where c = VT/P